Supposedly "new" projector, LAMP warning, no image

Hi! I just unboxed a supposedly "new" Amazon-bought projector, a new box, all manuals and cables present, in a pristine state, and even a brand-new smell. It turned on dimly for a few seconds, then the LAMP light came on and the unit did not turn on again. Fan spins and the beep starting tone is heard. Took the cover off, projector looks completely new. Took the lamp out, completely new, with no heat marks, and measured resistance between terminals: zero ohms. No smells or signs of use inside the projector.

I have intermediate electronics knowledge, but no projector experience. Is there any other thing I can try, for example, a way to test the lamp ballast output?

Thank you

PS: The projector is outside of the returning window time.

PS: Tried connecting an RS-232 cable, but there is no response. Doesn't matter too much, because there is no command to reset the lamp counter or do something useful for my problem.